Bounds of optimal learning.

Belavkin, Roman V. ORCID: https://orcid.org/0000-0002-2356-1447 (2009) Bounds of optimal learning. In: 2009 IEEE International Symposium on Adaptive Dynamic Programming and Reinforcement Learning, March 30 – April 2, 2009, Sheraton Music City Hotel, Nashville, TN, USA. . [Conference or Workshop Item]

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Abstract

Learning is considered as a dynamic process described by a trajectory on a statistical manifold, and a topology is introduced defining trajectories continuous in information. The analysis generalises the application of Orlicz spaces in non-parametric information geometry to topological function spaces with asymmetric gauge functions (e.g. quasi-metric spaces defined in terms of KL divergence). Optimality conditions are formulated for dynamical constraints, and two main results are outlined: 1) Parametrisation of optimal learning trajectories from empirical constraints using generalised characteristic potentials; 2) A gradient theorem for the potentials defining optimal utility and information bounds of a learning system. These results not only generalise some known relations of statistical mechanics and variational methods in information theory, but also can be used for optimisation of the exploration-exploitation balance in online learning systems.

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